Question: Solve for $x$ and $y$ using elimination. ${x+4y = 33}$ ${-x-5y = -40}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-y = -7$ $\dfrac{-y}{{-1}} = \dfrac{-7}{{-1}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {x+4y = 33}\thinspace$ to find $x$ ${x + 4}{(7)}{= 33}$ $x+28 = 33$ $x+28{-28} = 33{-28}$ ${x = 5}$ You can also plug ${y = 7}$ into $\thinspace {-x-5y = -40}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(7)}{= -40}$ ${x = 5}$